Calculating device



A. H. RADFORD. vCALCULATING DEVICE.

APPLICATION FILED APRZY, 1921.

Patented Mar. 21.1922.

2 SHEETS-SHEET i.

ALPHONSE. HRADFO RD gmmm A. HQE/1.9mm.

CALCULATLNG DEVCE. APPLICATION FILED APR-.27,1921.

9m 2. 92 1H Lw. s! .mw d2 .m .m D..

A'LPHoNELHQRADFoRD 3mm.

Guanda;

UNrri-:D STATES PATENT OFFICE.

ALPHONSE H. RADFORD, OF PHILADELPHIA, PENNSYLVANIA.

CALCULATING DEVICE.

'T0 aZZ w/Lo'm. it may concern:

Be it known that I, ALPHONSE H. RAD- ronn, a citizen of the United States, residing at Philadelphia, in the county 'of Philadelphia and State of Pennsylvania, have in-` vented certain new and useful Improvements in Calculating Devices, of which the following is a specification.

The object of my invention is to provide a novel calculating device by means of which certain calculat-ions may be made with much less time and effort than has been possible with the aid of tlie means and devices heretofore used to attain the same ends.\\

The invention aims to reduce the time and effort which has been required to ascertain,- the total number of elemental parts and fractions thereof of quantities of such parts and their fractions represented by a plurality of factors each of which represents a certain number of like quantities which' differ from quantities represented by other factors, the Yelemental parts of different quantities thereof represented by different factors being governed lby or ascertainable from different fixed values existing between different elements of a series thereof which is common to all the factors.

The invention may be employed in widely varying elds for many useful purposes among which calculating the total number of miles and the fractions thereof represented by the tickets used by passengers traveling varying distances, in both directions, over a railroad, between different stations thereof, where -tbe stations are` numerous.

lilith the foregoing object iu view, the invention consists in. the novel combination and arrangement of the, elements of the device`r as will be hereinafter described and claimed.

ln the accomminyingr drawing,

Figure 1 is a face view of a calculating device embodying my invention.

Figure. 2 is a view similar to Fig. l after placing thereon certain figures in reaching a conclusion'by the aid of the device, as will bel hereinafter explained.

AReferring to the drawings, S designates a sheet of paper or other suitable material having inscribed on its face the following' elements; a first group of numerals or factors a, a second group of numerals or factors Specification of Letters Patent. Patented luar, 21, 1922.

1921. seriai'n. 464,956.

Z), a first series of series of designa-tors multipliers e, a second short series of multiphers f', a first long series of multipliers g and a second long series of multipliers Zz'.

vThe f irst series of designators c are arranged in a certain prescribed order from aV commencing designator A to a. Aterminal designator J g andthe second series ofdesignators 'f Z correspond in number and character with the designators of the series c, and they are arranged in like order from a com-- mencing designator A to a terminal nator J.

'The factors of thevtirst groupe thereof are arranged in a set of vertical lines t' and a set vof horizontal lines j which cross the designators c, a second vertical lines a', the same factors of the group a being arranged in the lines of. the two sets 'af and y' and in the regions where the lines cross each other; and the factors .of the second group Z2 thereof are arranged in a set of vertical lines Ze anda set of horizontal lines Z which cross same factors of the group b being arranged in the lines of the two sets L and Z and in the regions where the lines cross each other.

To quickly and properly locate the factors a and b in the sets of lines v, j and Z1, Z. respectively, thereof, I inscribe upon the face of the sheet S intersecting vertical and horizontal lines enclosing squares or other suitably shaped elds arranged in horizontal and vertical rows and divided by a diagonally directed row m thereof into first and second groups or sections containing the factors a and b, respectively.

Each set of factor lines i, j, Zr, Z havevthe factors thereof progressively increasing in number; the two sets of factor lines z' and 7c, omitting the long factor line Zr at the left hand side of the set thereof and the long factor line i at the right hand side of the set thereof, are arranged opposite to or form, in effect, continuations of each other inversely of the order in which their factors increase in number; and the two sets of factor lines j and Z, omitting the long fact-or line j. at the top of the set thereof and the l long factor line Z at the bottom of the set thereof, are arranged opposite to or form, in effect, continu-ations of eachother inversely of the orde-r in whichtheir factors increase in number.

d, a first short series of the vertical lines 7c, the

lines i and lo in the order in which the facy tors of the lines i increase 1n number, and 1n-.

vers'ely of the order in which-thefactors of the lines It' increase in number.

The designators of the second series l thereof'are 'related to the horizontal lines of factors j and Z, one designator to a line of each set, omittingthe terminal designator J for the set of factor lines j, and omitting the commencin designator A for theset of factor lines Z, t. e series of`designators d extending from its commencing designator A to its terminal designator J through the two sets of factor lines j and Z inversely of the order in which the factors of the lines j in- 25 crease in number, and in the order in which the factors of the lines Z increase in number.

The set4 of factor lines-vf of the factor 'group i and the set loffactor lines Z of the factor group bhavethefactois thereof progressively increasing .in number from the commencing deeignator A to the terminaly designator J of each series c and cl; and the set of factor lines j of the factor. group c and the set of factorlines k for thefactor group b haveV the factors thereof progres` sively increasing .in number from the teri minal designator J to the commencing desir,-

nator' A ofeach series c and al.'

For convenience` of reading, the sei-ies ofy designators c are arranged in a horizontal line above' the vertxcalrows of squarescon- A-`tamm the factors, one, above each vertical 'row o squares, and,v also in alinement with the lines of factorsi'i and c, and the series'of .designators d are arranged in a 'vertical ,line adjacent to'onel end of the horizontal 't rows of squares containing the factors, one

adjacent to each horizontal row of squares, and'also in alinement with the lines of factorsjandl...

The first short series of multipliers e cor- Arespondin number, less two, with the series of designators vvc and they are related thereto" one to eachfdesignator c and its factor line ,omitting the commencing deslgnator A and the terminal designator J and its correspondingv factor line i; and the second short seriesof multipliers f correspond in number, lless two, with vthe series of designators c and Vthey are* related thereto one to l cach designator c and its factor line il: omitting the terminal designator J and the commencing designator. A and its'corresponding `factor line i I.

The first'longvseries oflmultiplicrs y cor-V series thereof.

respond in number, les?,I one, with the series of designators d, and they are related thereto oneto each designator d and its factor line j omitting the terminal designator J and the second long series of multipliers It Correspond in number, less one, with the series of designators d, andthe3T are related thereto one to each designator Z and its factor' line l, omitting the commencing designator A.

For convenience of reading, the multipliers of the four series thereof e, f, g and It are arranged opposite to or in alinement with the lines of factors and the designators of the two series thereof to which they are related, as hereinbefore described.

Each multiplier of the short and long series thereof e and g related lto the factor lines t' ,and y', respectively, of the first factor groupe represent a fixed value existing between its 'designator and the terminal designator of its series, and the multipliers c land g progressivelyincrease in value toward the commencing designators of their series @and (Z, respectlvely; and each multiplier of the short and lon series thereof f and 7i rev lated to the actor lines and Z, respectively, of the second factor group o represent a fixed value existing between its designator and the commencing designator ofits series, and the multipliers f and/i progressivelypincrease in value toward the termi@ nal designators of their series c and (l, re-

` spectively.

The two series of designators c and al are alike in every particular excepting their relation to the lines of factors yand the multipliers and they designate or represent 4pie cisely the sameseriesof things having the same values existing between them.

There exists between the commencing designator A and the terminal designator J of each series thereof an entire fixed value equal to the value expressedby the highest multiplier of the two long series g .andli thereof and this entire fixed value ,is divided into quantities of elemental parts and fractions thereof by the designators which intervene between the commencing designa tor 'A and the terminal designator J of each Such divisions of the entirevalue exist between adjacent,VA designators` and the part of the entire fixed value between any twonext adjacent designators of either series c and (l thereof is the difference in value between the two multipliers, related thereto or aligned therewith, of any one of the four series ofv multipliers e, f., g and li; in other words, the difference in `value between each two adjacent multipliers of each of the,

series e, f, q and l1, thereof represent a fixed value Nexis' ing between the designators c and d related theretofor alined therewith.

Each factor numeral of each group a and ,o 'stands for and 4expresses a number of quantities of either the entire fixed value between the commencing designator A and the terminal designator J or a fractional part of the entire value existing between two of the designators, in accordance with the position'of the factor in the vertical and horizontal lines thereof and its relation to or alinement with the designators of the two series c and Z thereof, as hereinafter eX- plained.

F or convenience in using the device, l inscribe on the sheet S certain lines enclosing the multipliers of the four series thereof e, 7', g and lz, and enclosing rows of squares or suitably shaped fields n, y), y, r, s, t, u and c, two adjacent to each multiplier and alined therewith and with their related, designators and lines of factors, as shown in lthe drawings.

I shall now describe the manner in which the device is used to accomplish its object in connection with calculating the totalnurnber ofk miles and fractions thereof represented b'y the tickets issued from different stations of a railroad within a given period of time for travel, in both directions over the same, between many varying stations as starting ,and finishing points. When the device is used in this connection, the-stations of the railroad will constitute and be arranged in the series of designators c in the order in which they occur from the commencing station to the terminal station of the railroad and the actual names of the stations will be used in lieu of the alphabetieal designators shown in the drawings. We may, therefore, assume that the stations are named A, B, C, D, etc., from the commencing station A to the terminal station J of the first series c thereof. The second series (Z thereof is precisel)7 like the first series, excepting as to their position on the sheet S, standing for and representing precisely the same things that the first series c sta-nds for and represents. i

The numerals of the long series of multipliers 7i stand for and express the distances in miles and fractions thereof between their respective stations d and the commencing station A; i. e., 2.3 miles between A and l, 4.0 miles between A and C, 5.5 miles between A and D, and so on thrt'iughout the series it, the highest multiplier of the series expressing the length of the railroad or the distance between the commencingl station A and the terminal station J.` inversely,

the-numerals oft-he series of multipliers 1f/ stand for and express the distances in miles and fractions thereof between the respective stations d and the terminal station J; i.e., 1.8 miles between J and l, 4.6 miles'between J .and H, 9.0 miles between J and G, and so on throughout 'the series y, the highest multiplier of the series ,f/ being 'the same the highest multiplier of the series l and expressing the length of the railroad or the distance between the terminal station J and the commencing station A( The numerals of the short series of multipliers f stand for. and express the distances in miles and fractions thereof between their respective stations'c land the commencingr station A, omitting the terminalstation J; and the numerals of the short series of multipliers e stand for and express the distance-s in miles and fractions thereof between their resjpective stations c and theterminal station It will now be understood that the difference in miles between each two adjacent multipliers of the series e, f, g and )t thereof is the distance. between the two adjacent stations related thereto or alinedtherewith.

Now, the total number of tickets issued from each station of the railroad during the period of time being accounted foris represented by the sum of the\two groups of factor numerals placed within the squares n. and 7),' and these two groups of factor numerals are placed within the-squares and related to the duplicate series of stations c and l in accordance with the relation of the tickets thereto as follows: All tickets issued b beneath or alined with station A of the first series c, all tickets issued from station B are placed in the vertical row of squares a and Z) beneath or alined with station B of the first series c, all 'ticket-s issued from station- C are placed in the vertical row of squares a and beneath or alined with station C, and so on to the end of the series of stations. The tickets issued from each station of the series c are placed opposite to or in alinement with the stations of the series (Z to which they are issued; in other words A station issues 5 tickets to B, 8 tickets to C. 9 tickets to D, 4 tickets to E, 8 tickets to G, 6 tickets to H, Q'tickets to l, and l2 tickets to J, and the representative factor numerals of these ticket issues are placed within the first vertical row of squares L, as shown invthe drawings; B stav tion issues S tickets to A, 3 tickets to C, 4 tickets to I), (i tickets to E, 14 tickets to F, 5 tickets to G, 3 tickets to ll, 7 tickets to I,

and 4. tickets to J, and the representative" It will thus be seen. that eachticket-representing fiuwtor-numeral (if the twogroups aand stands-for and represents a corresponding number of m1les, or miles and placed by representative ioo 7 tickets to ll",

the series of i together', and the sums of the res ective4 lines of the sets z', j, la and Z are place within the adjacent squares ii, g, y) and r which are alined therewith, respectively,'as shown in Fig. 2. The respective .sums entered in the squares a,g,p and rare multipliedby the multipliers of the sets e, g, j' and Ii which are alined therewith, respectively, and the products resulting therefrom are placed within the adjacent squares a, u, t and/1,- which are alined therewith, respectively, as shown in Fig. 2. The products within the squares s and t f rom the two short series of multipliers e and f, respectively, are added together in any coiivenientmanner, and the sum 1c thereof is placed upon the sheet S. The products within thesquares u and c from the two long series of multipliers g and i, respectively, are added together in any convenient manner` and the simi 1/ thereof is placed upon the sheetS over the suiii w. sum y' and the result z is the total number of miles represented by the tickets, or numerals of the twogroups a and b, or the total nuin- Y ber of'niiles traveled by the passengers using the tickets.

Iliave discovered that the lcalculating device shown and described herein permits the result described hereinto be reached inA much l less time and with much less effort than is required with the use of the means 4hereto-` fore employed for the same purpose; the savingin 'time and effort being accomplishedA by the reduction of space occupied b v the' work, the reduction of the number of entries of designators or stations, the reduction-of the number of entrles of multipliers or distances, the reduction of the number of additions of figures and, Ji'xrticularl the great reduction of the num ier of mu tiplications of figures. The proportionate saving of time and effort is greatly increased withtlie increase in the vnumber of desgnators or stations of the series thereof, and, whenit is considered 'that the number 0f stations cfa4 railroad line is usually greatly in excess yof the number of desi mators Voli stations shown.. and described herein, thefvalue of the rdevice` and the great savingpeiected, thereby in t railroad and analogous work will` be ap'-,

prec-interi. i 4 i i The reduction of the 'work neoessar to accomplish the end correspondingly re' aces' the chance of errors occurring inthe work;

The sum w `is now subtracted from the between each scribed order from a commencing designator to a terminal designator; a second series i of like designators arranged in like order from a commencing designator to a terminal designator; a first group and a second` group of factors representing numbers of quantities of elemental parts of fixed values existing between designators of each of said series, each group being arran ed in two sets of lines which cross each ot er, the same' factors of each group being arranged in the lines`of each of its sets and individually in i the regions 'where the lines cross each other,

one set of'lines of each group-being stationed in the relation of one line to a designator of the first series; thereof, the other set of lines of each group being stationed lin the relation of one line to a desgnator of the second series, one setof factor lines of each factor group having the factors thereof progressively increasing in number from the cornmencin to the terminal designatorv of each series tiereof, and the other set of factor lines of eaclr factor group having the factors thereof progressively increasing in number from the terminal to the commencing designator of each Aseries thereof; a long series of' multipliers for one set of factor lines of each factor group, the multipliers of each long seriesj being stationed in the relation of one multiplier toa'liiie of its sets of factor lines 1 and one -multiplier to a' designator of. the

first series thereof, omitting the commencing designator for the factor'lines of one Afactorgr'gup and omittingthe terminal des- .ignator for the factor lincso the-other fac- Ator group; a short series of multipliersrfor thc other set of factor' lines of each factor rroiip, the multipliers ofeach short series being stationedjn the relation'of one multiplier to a line of its set of factor lines. and

' one multiplier to a designator of the second series thereof, omitting the 'commencing and terminal desgnators'for the factor lines of 4each group reach multiplier of the' short and ,long series thereof, related to therst. factor group, re resentinga fixed value between its designation and `the terminal designator of its` series, `tlief'multipliers` progressively -increasingff in value;v toward g.; the commencing desi fn "hmultiplie'r of the short atedjthe second fixed value bey p y j` the commencing of-i series, the multipliers progressively' increasing in f value-toward the terminal designator; the difference in value two' adjacent multipliers of each of the long and short series thereof representing a fixed value existing between their designators; whereby the total number of elemental parts of the quantities thereof represented bythe factors of the two groups may be ascertained by multiplying, by the multipliers of one long series and one short' series, the sums ofthe factors of the lines thereof of the first group related thereto, by multiplying by the multipliers of the other long series and the other short series, the sums ofthe factors of thelines thereof of the second group related thereto, and subtracting the sum of the products of the two short series of multipliers fromrthe Sum of the products of the two long series of multipliers.

2,-A graphic calculating device comprising a sheet having inscribed thereon vertical and-horizontal intersecting lines enclosing squares arranged in vertical and horizontal rows or lines; a vertical series of designators corresponding in number with the horizontal rows of squares and stationed one adjacent to each horizontalrow and arranged in prescribed order from a commencing designator to a. terminal designator; a horizontal series of like designators corresponding in number with the vertical rows of squares and stationed one adjacent to 'each vertical row and arranged in like order from a commencing designatorto a terminal designa' tor; said rows of squares being divided by a diagonal row thereof into two divisions; a first group of factors individually occupying individual squares of one division thereof; a second group of 4factors individually occupying individual squares of the other division thereof; the factors of each group representing numbers of quantities of elemental parts of fixed values existing between designators of each of said series; a long vertical series of multipliers for each grou of factors, stationed one adjacent to eac horizontal row of squares 'and one adjacent to each designator ofthe vertical series,

omitting the commencing designator and the top row for the series of multipliers of one group and omitting the terminal designatoi" and the bottom row for theseries of multipliers of the othervgroup; a short horizontal series of multipliers for each group of factoi's,'statione'd one adjacent to each vertical row of squares and one adjacent topliers progressively increasing in'value toward the commencing designator; and each multiplier of the short and long series thereof related to the second factorgroup representing a fixed value between its designator and the commencing designator of its series,

thefmultipliers progressively increasing in value toward the terminal designator; the difference in value between each two adjacent multipliers ofL each'I of the long and short series thereof representing a fixed value existing between their designators; whereby the total number of elemental parts of the quantities thereof represented by the factors of the two groups may be ascertained by multiplying, by the multipliersof one long series and one short series, the sums of the vertical and horizontal rows if factors in the rows of squares of one divisitinrelated thereto, by multiplying, by the multipliers of the other llong series and-the other short series, the sums of the vertical and horizontal rows of factors in the rows of squares of of the products of the two long series of multipliers.

ALPHONSE RADFORD. 

